\newproblem{lay:5_3_1}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 5.3.1}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Let $A=PDP^{-1}$ with $P=\begin{pmatrix}1 & 2 \\ 2 & 3\end{pmatrix}$ and $D=\begin{pmatrix}1 & 0 \\ 0 & 3\end{pmatrix}$. Calculate $A^4$.
}{
   % Solution
	If $A=PDP^{-1}$, then
	\begin{center}
		$\begin{array}{rcl}A^4&=&PD^4P^{-1} \\
		   &=&\begin{pmatrix}1 & 2 \\ 2 & 3\end{pmatrix}\begin{pmatrix}1^4 & 0 \\ 0 & 3^4\end{pmatrix}\begin{pmatrix}-3 & 2 \\ 2 & -1\end{pmatrix}\\
			 &=&\begin{pmatrix}321 &-160 \\ 480 & -239\end{pmatrix}
	  \end{array}$
	\end{center}
}
\useproblem{lay:5_3_1}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
